Can I update an Mac App purchased by a different Apple ID?

No. You need his username and password to update.

As alternative you can create an account for your company, and then download Xcode again.

I recently ran into this issue in a different context. I changed my developer appleID and had xCode registered under the defunct one. When I upgraded to Mavericks, Xcode wouldn't update, since I'd downloaded it from the Apple store under defunct AppleID.

I removed the association with the defunct appleID by removing the receipt from Xcode:

• Control-click Xcode app and "show package contents".
• Move the _MASReceipt directory to the trash in order to dis-associate Xcode with the old AppleID (you'll need your Mac's admin password).
• Restart Apple store and "install" (rather than upgrade).

The net effect: Xcode will "install" (upgrade) but under your preferred AppleID.

You do NOT need your ex-employee's personal AppleID account for this, but you do need admin rights on the machine.